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1 1. Phylogenetic Nomenclature We followed Sereno et al. (2004) 1 and Ezcurra ( ) with respect to the definitions of several higher-level theropod taxa used in this paper: Averostra, the least inclusive clade including Ceratosaurus nasicornis and Neornithes Tetanurae, the most inclusive clade including Neornithes but not Ceratosaurus nasicornis Aves, the least inclusive clade including Neornithes and Archaeopteryx lithographica Coelophysoidea, the most inclusive clade including Coelophysis bauri but not Neornithes. Ceratosauria, the most inclusive clade including Ceratosaurus nasicornis but not Neornithes. Abelisauroidea, the least inclusive clade including Carnotaurus sastrei and Noasaurus leali. Noasauridae, the most inclusive clade including Noasaurus leali but not Carnotaurus sastrei. Abelisauridae, the most inclusive clade including Carnotaurus sastrei but not Noasaurus leali. 1

2 2. Ontogenetic stages of the Limusaurus inextricabilis holotype and referred specimens The Limusaurus inextricabilis holotype is estimated to be 170 cm in total body length based upon the length of the nearly complete skeleton and an estimate for the length of the missing distal caudals. All observed cranial elements except the left and right parietals are unfused. All observable sutures between the centra and neural arches are closed. The scapula and coracoid are fused to each other, but the suture is visible. The pelvic elements are not fused to each other. The astragalus and calcaneum are fused to each other, but not to the tibia. The distal tarsals remain separate. The referred specimen IVPP V is 15% larger than the holotype (based on tibiotarsus length). It is similar to the holotype in the extent of skeletal fusion except that the astragalus-calcaneum complex is fused to the tibia. As a whole, the evidence from osteological fusion suggests that neither specimen is a juvenile. The other referred specimen IVPP V16134 is probably at the same ontogenetic stage as the Limusaurus inextricabilis holotype, given that they are about the same size and display the same extent of skeletal fusion. We also estimated the ontogenetic stage of IVPP V by examining a thin-section from the mid-shaft of the fibula. The bone (photographed with polarized microscopy) is heavily infiltrated with fungus and this led to some destruction of the microstructure (black blotches and root-like patterning are visible). Even so, the primary and secondary microstructure including growth lines is present in sufficient detail to allow histological characterizations and determination of the individual s age. The inner half of the cortex is mostly composed of dense haversian bone (HC = round haversian canals in figure 1c). In other words, the primary bone has been heavily remodelled. This is common in dinosaurs as well as in extant mammals and birds 3. There are multiple layers of endosteal bone (EB in figure 1c) lining the medullary cavity. Coupled with the dense haversian structure, this points to the individual s being of advanced age, rather than a juvenile 4. The primary bone that is present in places shows that during the majority of development a longitudinally vascularized, fibro-lamellar bone type predominated. This is common in small dinosaurs 3, 5. Four definitive lines of arrested growth (aka: growth lines; white vertical arrows) are present. No more than one line was originally present where the medullary cavity now exists. This places the age of the animal at 5 years, meaning that it died in its sixth year of life. This is consistent with subadult age in a small dinosaur. Note that the three outermost growth lines locally expand into layers of lamellar bone, as is common in theropod dinosaurs. The outermost zones (areas of bone between the growth lines) are approximately 1/2 to 1/3rd the radius of the earlier zones. This indicates that the animal's growth was beginning to slow at the time of its demise, but that growth was still incomplete. Together with the dense haversian bone, extensive and multiple endosteal bone deposition events, and the fact that a larger individual is known from the same site, this finding points to the conclusion that the individual was a young adult - probably between the exponential and stationary phases of development. 2

3 3. Morphological comparisons Limusaurus inextricabilis has the following ceratosaurian features 6-8 : skull relatively tall, antorbital fenestra relatively small, premaxilla with short maxillary process and long and robust nasal process, maxilla contributing to ventral border of external naris, nasal with anterolateral margin slightly convex laterally and posterolateral margin contributing to antorbital cavity, lacrimal with anterior process short and slender relative to ventral process, external mandibular fenestra large, dentary short compared to postdentary elements, angular positioned significantly anterior to posterior end of mandible (Fig. S1a), proximal head of humerus bulbous, deltopectoral crest long and obliquely oriented, ossified carpals absent (Fig. S1c), distal end of pubis terminating in a large, caudally expanded foot, ischial antitrochanter large (Fig. S1d), anterior surface of distal femur with shallow extensor groove, and pedal unguals with two lateral grooves. Among ceratosaurs, Limusaurus inextricabilis shares some derived similarities with most other ceratosaurs except Elaphrosaurus 6 : post-axial cervical neural arches pneumatic, dorsal vertebrae with parapophyses on laterally projecting stalks, humerus non-twisted, medial epicondyle of femur flange-like, cnemial crest of tibia long anteroposteriorly, fibular M. iliofibularis tubercle large, calcaneum with large tibial facet, and main body of astragalus anterior to tibia. Limusaurus lacks the following derived features that are present in Ceratosaurus and more derived ceratosaurs 6 : premaxilla dorsoventrally taller than anteroposteriorly long below external naris, nasals fused, frontals and parietals fused to each other and fused across midline, infratemporal fenestra large, quadrate and quadratojugal fused (Fig. S1a), pleurocoel present at cranial end of axis, pneumatic foramen or foramina in the axial neural arch, cranial margin of scapulocoracoid smoothly curved and uninterrupted by a notch at the scapulocoracoid contact (Fig. S1b), distal humeral condyles flattened, and proximal end of metacarpal I loosely appressed to metacarpal II. But Limusaurus appears to be more derived than Ceratosaurus in some features: proportionally shorter forelimbs, shorter forearms, and shorter manus (forelimb less than one-fifth of hind limb length, metacarpus less than one-third of forearm length), long coracoidal posterior process, prominent coracoidal tubercle, exceptionally high acromion process sharply deflected from unusually broad and distally unexpanded scapular blade, prominent furrow posterior to scapulocoracoid suture on lateral surface of scapula (Fig. S1b), and laterally inset pubic boot. Interestingly, in some phylogenetic analyses 9, 10 ceratosaurs represent a paraphyletic group and Ceratosaurus is found to be more closely related to tetanurans than to other ceratosaurs. Limusaurus shares some similarities with noasaurids, including a suite of maxillary features, cervical neural spines positioned relatively anteriorly on corresponding centra (though not as anteriorly positioned as in noasaurids), and metatarsal II very slender for most of its length (also in Elaphrosaurus). Among noasaurids, Limusaurus is similar to Masiakasaurus 11 in the following characters: down-turned anterior end of dentary with convex buccal margin (Fig. S1a), manual unguals with two vascular grooves on each side, proximal half of femur sub-triangular in cross section, and metatarsal IV with transversely very narrow distal end compared to those of metatarsals II and III (also in Deltadromeus) 12,1 Limusaurus and Elaphrosaurus are similar to each other in many features, most of which are plesiomorphic features also seen in coelophysids 6, 8 : cervical vertebrae significantly elongate (also present in coelophysoids), small, medially inclined ilium with ventral margins of both preacetabular and postacetabular blades laterally flared to form shelves, brevis fossa extensively laterally exposed, and a blunt, medially curved posteroventral process (Fig. S1d), and hind limbs elongate. Furthermore, Limusaurus is similar to coelophysids in the following 3

4 features: prominent rim on external antorbital fenestra, external naris proportionally large and posteriorly extended, lacrimal ventral process with strongly posteriorly expanded distal end, angular forming nearly entire ventral border of external mandibular fenestra, axial parapophysis reduced, axial diapophysis absent, and ischium terminating distally in a knoblike swelling. It is worth noting that some of these features are also seen in noasaurids. In addition, Limusaurus shares many derived similarities with tetanurans 13. These include external naris large and posteriorly located, scapular acromial process prominent, scapulocoracoid notched between acromial process and coracoid, ventral coracoid process well-developed, fibular condyle strongly offset from tibial cnemial crest, distal end of tibia expanded to contact calcaneum, fibula closely appressed to tibia along entire length of the main shaft, and pedal digit I distally located. The distribution of morphological characters during the early divergent period of theropod dinosaur evolution is fairly complex 14, 15. This is further demonstrated by the anatomy of Limusaurus, which has a combination of the primitive and derived characters that are present in three major theropod groups. Much of the uncertainty concerning character evolution close to the base of the theropod tree is caused by a large amount of missing data in early theropods, particularly ceratosaurs and basal tetanurans. The prevalence of homoplastic evolution also helps to explain the complex pattern. A comprehensive analysis including more taxa and characters is needed to reconstruct the relationships among basal theropods and better understand the early evolution of theropod dinosaurs. 4

5 Figure S1. Limusaurus inextricabilis selected elements. a, Skull in lateral view; b, Left scapulocoracoid in lateral view; c, Left manus in dorsal view; d, Pelvis in lateral view. Abbreviations: a, angular; ap, acromion process; bf, brevis fossa; ct, coracoid tubercle; d, dentary; dc, deltopectoral crest; emf, external mandibular fenestra; en, external naris; f, frontal; fl, flange; lf, longitudinal furrow; ils, lateral shelf on ilium;?isf, ischial foramen; lr, lateral ridge; ls, lateral shelf; mci-iv, metacarpals I-IV; mf, maxillary fenestra; n, nasal; p, parietal; pf, prefrontal; pfe, pubic fenestra; pm, premaxilla; po, postorbital; pp, posterior process; qj, quadratojugal; r, radius; rc, radial condyle; sac, supraacetabular process; u, ulna; uc, ulnar condyle. 5

6 4. The manus in Limusaurus inextricabilis and other non-avian theropods. The manus of Limusaurus inextricabilis is not preserved completely in any specimen, but the three specimens reported here allow a nearly complete reconstruction. Digit I, comprising only a greatly reduced metacarpal, is preserved in articulation in IVPP V16134 (Fig. S2) and in a disarticulated condition in IVPP V Digit II is completely preserved in articulation in the holotype and disarticulated in V12594, and comprises a robust metacarpal and three phalanges. The morphology of metacarpal II varies between the two specimens: in the holotype the distal end is more strongly asymmetric and in V12594 there is a well developed flat surface, dorsodistally bordered by a small flange, in proximolateral contact with metacarpal III. Digit III is incompletely preserved in the holotype, retaining only the metacarpal, part of the penultimate phalanx, and the ungual phalanx, and in V12594 it includes the disarticulated metacarpal and three phalanges, the distal two in articulation. The articular surfaces on the distal surface of phalanx I and the proximal surface of the penultimate phalanx closely match, indicating that an unpreserved intermediate phalange was absent. Digit III therefore includes a metacarpal slightly longer than metacarpal II and more gracile, and three phalanges, of which the ungual phalanx is rotated 90 degrees medially and the penultimate phalanx has an unusual proximal surface whose ventral portion projects further proximally than does its dorsal portion. Of digit IV each specimen preserves only a portion of the slender metacarpal, the proximal half in the holotype and the distal half in IVPP V The existence of an articular surface on the distal end of the latter indicates that phalanges were present, but their number is uncertain. Coelophysids possess three well-developed medial manual digits, a reduced fourth digit, and at least in Coelophysis bauri 16 a vestigial metacarpal V (Fig. S3). Their manual phalangeal formula is ?-0. Dilophosaurus closely resembles coelophysids in its manual morphology, including the presence of a vestigial metacarpal V, but also differs in several features including a more slender metacarpal I and proportionally shorter phalanx I-1. Non-avian tetanurans mostly have three well-developed digits, with a phalangeal formula corresponding to that of the medial three digits of more basal theropods. A vestigial fourth metacarpal has been reported in several non-avian tetanurans 13, 17, 18. A number of proposed tetanuran synapomorphies can be identified in the manus under the assumption that the three digits correspond to the medial three digits (I-II-III) of pentadactyl more basal theropods, including metacarpal I much shorter than metacarpal II 13, a substantial, oblique contact between metacarpals I and II 9, the base of metacarpal III set on the palmar surface of metacarpal II, and metacarpal III with a triangular proximal articulation 13. Interestingly, if one accepts the II-III-IV hypothesis for the three manual digits of tetanuran theropods, most of these tetanuran synapomorphies lose their validity because the same features are seen in metacarpals II-IV of non-tetanuran theropods. The large articular surface on the lateral side of metacarpal I is bounded dorsally by an elongate flange in tetanurans (Fig. S3). A similar, slightly shorter flange is seen on metacarpal II in Limusaurus, bordering a proportionally slightly smaller articular surface on the lateral side of metacarpal II (Fig. S3). In more basal theropods such as Herrerasaurus (Fig. S3) and Dilophosaurus, an even shorter flange is present on the dorsolateral corner of metacarpal II and forms an overlapping contact with metacarpal III. Similarly, metacarpal IV of ceratosaurs, Dilophosaurus, and more basal theropods is similar to metacarpal III of tetanurans in having a sub-triangular proximal outline, in being very slender compared to the more medial metacarpals, and in being set on the palmar surface of the adjacent metacarpal. 6

7 Furthermore, metacarpal III has a distinct dorsolateral process on its proximal end in ceratosaurs, Dilophosaurus, and more basal theropods, comparable to a similar process on the middle metacarpal of basal tetanurans. These similarities suggest that the three metacarpals of tetanurans correspond to metacarpals II-IV, rather than I-III, of more basal theropods. Finally an extensor pit is absent in metacarpal IV of ceratosaurs, Dilophosaurus, and more basal theropods, as in the lateral metacarpal of tetanurans. The absence of an extensor pit is, however, likely to be correlated with the slenderness of the metacarpal and thus may not be good evidence supporting the II-III-IV hypothesis. 7

8 Figure S2. The ventral surface of a partial, articulated left forelimb of Limusaurus inextricabilis (IVPP V16134) embedded in silicone. Arrow points to a reduced metacarpal I. 8

9 Figure S3. Theropod manual morphologies as represented by several non-avian theropod taxa. a, Herrerasaurus carpus in proximal view; b, Coelophysis manus in dorsal view; arrow points to metacarpal V; c, Dilophosaurus manus in proximal view (top) and ventral view (bottom; image reversed); arrow points to metacarpal V; d, Allosaurus manus in ventral view. 9

10 5. Select measurements of Limusaurus inextricabilis holotype Select measurements (in mm) of Limusaurus inextricabilis holotype Elements Mandible length 105 Dentary length 59 Snout length 55 External diameter 17 Antorbital fossa length 26 Posterior cervical vertebra length (C7) 45 Anterior dorsal vertebra length (D4) 26 Anterior caudal vertebra length (C2) 27 Middle caudal vertebra length (C12) 26 Left scapula length *95 Right humerus length 80 Right radius length 40 Right metacarpal II length 12 Right metacarpal III length 13 Left ilium length 140 Left ischium length 133 Left femur length 208 Left tibiotarsus length 249 Left metatarsal III length 155 Left pedal phalanx III-1 length 36 Left pedal phalanx III-2 length 26 Left pedal phalanx III-3 length 20 Left pedal phalanx III-4 length 21 * indicates the averaged length of the left and right elements # indicates the estimated complete length of a partial element 10

11 6. Phylogenetic analysis. Character list Characters 1-353: Taken directly from the Smith et al., 2007 matrix. The following characters were ordered because they contain nested state sets or more than two states, with one state as absent : 3, 8, 10, 24, 56, 61, 75, 89, 94, 104, 121, 130, 155, 162, 171, 176, 185, 257, 289, 294, 300, 322, 324, 331. Characters : Taken from Carrano and Sampson, The correspondences between this data matrix and the characters from the Carrano and Sampson matrix are listed in parentheses. Character ordering is indicated External surface of maxilla and nasal (Carrano and Sampson, 2008, #1): 0 smooth 1 sculptured 355. External surface of postorbital, lacrimal and jugal (Carrano and Sampson, 2008, 2008, #2): : 0 smooth 1 sculptured 356. Maxillary process of premaxilla (Carrano and Sampson, 2008, #3): 0 well-developed 1 reduced to a short triangle 357. Subnarial foramen (Carrano and Sampson, 2008, #4): 0 enclosed 1 reduced/open dorsally (reduced/open dorsally): 358. Height:length ratio of premaxilla ventral to external naris (Carrano and Sampson, 2008, #5): 0.5 to greater than Facet for nasal articulation on maxilla (Carrano and Sampson, 2008, #7): 0 shallow, anterolateral 1 socket, lateral 360. Anteroposterior length of maxillary-jugal contact relative to total maxilla length (Carrano and Sampson, 2008, #11): 0 less than 40% 1 more than 40% 361. Row of foramina on dorsal nasal surface (Carrano and Sampson, 2008, #13): 0 absent 1 present 362. Location of nasal-frontal contact relative to highest point of orbit (Carrano and Sampson, 2008, #15): 0 anterior 1 directly above 363. Condition of prefrontal in adults (Carrano and Sampson, 2008, #16): 0 separate 1 partly or completely fused 364. Skull roof dorsoventral thickness (Carrano and Sampson, 2008, #18): 0 thin, relatively flat 1 thickened 365. Skull roof ornamentation (Carrano and Sampson, 2008, #19)(ordered): 0 none 11

12 1 midline 2 lateral 366. Orientation of posterior edge of postorbital (Carrano and Sampson, 2008, #26): 0 vertical 1 sloped anteroventrally 367. Morphology of dorsalmost postorbital-squamosal contact (Carrano and Sampson, 2008, #28): 0 smooth 1 knob 368. Appearance of postorbital-squamosal contact in lateral view (Carrano and Sampson, 2008, #29): 0 contact edges visible 1 edges covered by dermal expansions 369. Lacrimal fossa (Carrano and Sampson, 2008, 2008 #31): 0 exposed laterally 1 covered by dermal ossification 370. Morphology of lacrimal along dorsal orbit rim (Carrano and Sampson, 2008, #33): 0 flat 1 raised brow or shelf 371. Morphology of jugal-maxilla contact (Carrano and Sampson, 2008, #34): 0 slot or groove 1 lateral shelf 372. Relative lengths of posterior jugal prongs (Carrano and Sampson, 2008, #36): 0 upper prong much shorter than lower 1 both prongs subequal in length 373. Dorsoventral proportions of quadratojugal prongs for jugal (Carrano and Sampson, 2008, #39): 0 narrow 1 deep 374. Overlap of quadratojugal onto quadrate posteriorly (Carrano and Sampson, 2008, 2008 #40): 0 absent 1 present 375. Ossification of interorbital region (Carrano and Sampson, 2008, #42): 0 weak or absent 1 extensive 376. Vagal canal opening (Carrano and Sampson, 2008, #44): 0 through otoccipital 1 onto occiput 377. Shape of opening for basisphenoid recess (Carrano and Sampson, 2008, #46): 0 ovoid 1 teardrop-shaped 378. Depth of indentation between basal tubera and basisphenoid processes in lateral view (Carrano and Sampson, 2008, #47): 0 deep notch 1 shallow embayment 379. Size of dorsal groove on occipital condyle (Carrano and Sampson, 2008, #49): 0 wide 1 narrow 380. Orientation of basioccipital-basisphenoid suture (Carrano and Sampson, 2008, #50): 0 oblique 12

13 1 horizontal 381. Shape of pterygoid articulation with basipterygoid process (Carrano and Sampson, 2008, #54): 0 tab-like 1 acuminate 382. Arrangement of jugal and pterygoid processes of ectopterygoid (Carrano and Sampson, 2008, #55): 0 oblique 1 parallel 383. Proportions of ectopterygoid (Carrano and Sampson, 2008, #56): 0 gracile 1 robust 384. Size of external mandibular fenestra (Carrano and Sampson, 2008, #58): 0 small to moderate 1 large 385. Prongs at anterior end of splenial (Carrano and Sampson, 2008, #62): 0 one 1 two 386. Shape of articulated dentary rami in dorsal view (Carrano and Sampson, 2008, #64): 0 Vshaped 1 U-shaped 387. Position of lateral dentary groove (Carrano and Sampson, 2008, #65): 0 at or above mid-depth 1 in ventral half 388. Visibility of paradental plates in medial view (Carrano and Sampson, 2008, #70): 0 widely exposed 1 obscured 389. Medial groove in paradental plates exposing replacement teeth (Carrano and Sampson, 2008, #71): 0 present 1 absent 390. Length of axial epipophyses (Carrano and Sampson, 2008, #74): 0 moderate 1 long 391. Ventral keel on anterior cervicals (Carrano and Sampson, 2008, #81): 0 present 1 faint or absent 392. Length/height ratio of mid-cervical centra (Carrano and Sampson, 2008, #86): 0 less than 3 1 more than Height of postaxial cervical neural spines (Carrano and Sampson, 2008, #87): 0 moderate or tall 1 short 394. Accessory fossa on dorsal surface of postaxial cervical transverse processes (Carrano and Sampson, 2008, #88): 0 present 1 absent 395. Shape of dorsal transverse processes in dorsal view (Carrano and Sampson, 2008, #89): 0 rectangular 1 triangular 13

14 396. Orientation of ventral margin of mid-sacral centra (Carrano and Sampson, 2008, #95): 0 horizontal 1 arched 397. Dorsal edge of sacral neural spines (Carrano and Sampson, 2008, #96): 0 as thin as remainder of spine 1 thickened 398. Pneumaticity of sacral neural spines (Carrano and Sampson, 2008, #98): 0 weak or absent 1 well developed 399. Proportions of anterior caudal neural arch base relative to centrum proportions (Carrano and Sampson, 2008, #100): 0 smaller 1 equal or greater 400. Contact between cervical vertebrae and cervical ribs in adults (Carrano and Sampson, 2008, #102): 0 separate 1 fused 401. Wing-like process at the base of the anterior cervical rib shafts (Carrano and Sampson, 2008, #103): 0 absent 1 present 402. Bifurcate cervical rib shafts (Carrano and Sampson, 2008, #104): 0 absent 1 present 403. Spacing between glenoid and posteroventral process of coracoid (Carrano and Sampson, 2008, #107): 0 moderate 1 close 404. Size of coracoid (Carrano and Sampson, 2008, #108): 0 shallow 1 deep 405. Longitudinal torsion of humeral shaft (Carrano and Sampson, 2008, #112): 0 absent 1 present 406. Length of humerus relative to femur length (Carrano and Sampson, 2008, #114): 0 >1/3 1 <1/ Contacts between pelvic elements in adults (Carrano and Sampson, 2008, #116): 0 separate 1 fused 408. Shape of dorsal margin of iliac postacetabular process (Carrano and Sampson, 2008, #120): 0 convex 1 straight 409. Morphology of dorsal surface of pubic boot on midline (Carrano and Sampson, 2008, #126): 0 convex 1 concave 410. Morphology of anterolateral muscle attachments on the proximal femur (Carrono and Sampson, #132): 14

15 0 continuous trochanteric shelf 1 distinct lesser trochanter and attachment bulge (this state includes derived coelurosaurs with a trochanteric crest): 411. Development of medial epicondyle of femur (Carrano and Sampson, 2008, #133): 0 rounded 1 ridge 2 long flange 412. Morphology and orientation of femoral tibiofibularis crest (Carrano and Sampson, 2008, #134): 0 narrow, longitudinal 1 broad, oblique Character 413: was added by the authors Manual digit 1 (ordered) 0 fully developed, with 2 phalanges 1 metacarpal reduced, no phalanges 2 absent 15

16 Matrix Marasuchus?????0???00?00??-???00?0??????????????????????????????00?????-??0?0??0?00?00????0??????????00???-??0???0??????0?????????????????????????????0???????????????????????????????0??0??1[0 1] ??0???00?00??????? ?0?0?0???? ?00000???0?000[1 2]?????????????????????????????????-????????????-?11??0??0??????????0??? Silesaurus?02? ????????00000?0?0??0?0020????00--????0?????0???????0???????????????????????00? ?00???????????0000????100??0?0? ? ??0000?00-100?000?0--000??0000?0??????????????100?0000[0 1] ??????0?????????????? ? ? ? ? ?? ???0000?00???????????????????????????????????????????????????????????? Herrerasaurus ? ? ? ? ?000000?? ? ???????? ? ? ? ? ? ? Eoraptor ?100?00? ?00?000? ?01000? ?0?0?000?0?000?00000?01??00?0?0??????????????????0???00?00?000???0??0?00???0????0--?0?0?0? ?0000?0?1?0010?00100?0?0?0000?00??0000???????? ??0???-00?1?0?000?00 000?0000??000000?0?000?1001??00?00-000??0000?0?0??0?0??0???0?00??0??00?0????0???0???000?000???00?000?000??000?10?0000? ??????????????????????????????????????? 0 Saturnalia?1?????????????????????????????????0????????????????????????????????????????????0???????????????????0?00-?????????????????????????????????????????0---0? ?00???000?01?00?? ???0?0????0??0???????? ?? ????????????????????? ??0? ? ???000??0??????????????????????????????1?????????????0???0?0?001000?? Plateosaurus ? ? ? ? [0 1]0? ?0000?0---0? ? ? ???????? ? [0 1] ??001000?[0 1] ? ???00?0??10? -??0?01??0?????? ?0 Abelisaurus 10?120010???????????000110?00?01??0?11?120--?2????10111?1011[2 3] ? ?011?01???20?00?1?000?00??????0?10??????????????????00??????????????1??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????111111? ?1111??1011??1???01???????????????????????? Acrocanthosaurus 16

17 ?? ?000? ? ? ? [0 1]1100? ?11[0 1] ?? ??110010?1? ? ?1???0010?[1 2 3]0??0?1?0?0??100110?0???????? ???0????????????0??????????[0 1]00? ?20??0110?01???21???????0??1??10?0011? ?1201?00000?000??00? ????1????0??0???????????????0011????00? Afrovenator 1?20?????[1 2]???????????0? ?????????1?1?110?000[0 1]01????????001100???00?1?????002???????????????????????????????????????????????????? ?100200?00??0[0 1]?10?1??????00?0???????0000?001?0?0??????????????????00000????????11110????0????000 00?0??0?00100[0 1] ?0??0110? ?201?0????0??002??0???01???111?02?0110?1???10?12 01??????0?00???00?????000000????????????????????00?????????????00?1??? Allosaurus ?01????? Archaeopteryx 0020?10[ ][0 1]2???10?1?1?00?0?10?111???01?0???0--?? ?????13?10??0?0??20?2???00?[0 1]01???0?0?102?1????01?????00????2??13???1?000001?01?0?00?11????1? ?1?1?????????0[0 1]??0???100??0?2??????111?10???0?11100?11?? ??100?01? ?? ?? ?010?1201?10? ?11??312?10??????????????1??[0 1]2?110?0211?100???0????1???0??????00??0?00?? ???????????????????????????????????????1??2 Aucasaurus???????????????????????2???0??????0?????2???????????????0???????1???0????????????????????????????????????????????????????????????????????????????????????????1???????????????????????[1 2]??????????????2??????????????0????1???1?1?1???????????????????????????1??1?????1???????1??1?????0??????????1???????????????1??1??????1??????111?1?????0???????0??111??????? 11?1111????2???1?1?????????????????????1?????1???0111?1?1?1? Baryonyx 10?? ?01?0?10?10?20000????21?10?01??00?2??0? ??000??0?01???????0? ? ?10?1001?0???????? ???????? ?01010? ?01010?1?100010?????????0???????????0????????[0 1]0? ???????????????0?01000????????10??010??1?00????0?0? ??0 1101?????010?????????0110?????????02???????????????????110111????1??????????00?????????????00?00???00???????????1???????0 Berberosaurus??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????1011?10?????????????????????????????11?????????????????????????????????????????????????????1????????????????????????????????????????????????????? ?0????????????1 1100???????????????????????????????????????????????????????????????????????????????????????????1??? Carcharodontosaurus 102????????????1??1???? ?0000? ?21?10110?111?111?1???1110?01?001?????? 17

18 ?????01??????11100????0101?111?????????????????????????????????1?1? ?0?000???????????????????????1???????????????????????????????????????????????????????????????????????????1???????????1?0??????????????120120??0?1?????????????????????????????????????????????????????????????????????????????????????????????????????????????? Carnotaurus ??? ? ? ?1? ? ?? ? ? ?-110?0?1???12?00???????0?? ???000?000 0?[0 1]00?????? ? ??????11??????????1????????????????????000? ?? Ceratosaurus ? ? ??1000? [0 1] ? ???????? ???? ?010??0???010?0010?1? ?? [1 2]10?110010? ?? ??0???0??? ? ?? [0 1]111 Coelophysis_bauri ? ? ?00000? ?00?0000?010?000??1???00?00?10??1?100?0101??? ? [0 1]200?1? ?? ???????? ? ?001??000 00? ? ? [0 1]11000? ??0?0000? ????????????0??0????11??0??????-01?11?1??0 Coelophysis_rhodesiensis ? ? ? ? ?10??1?10??01010??00000? ?0? ? ??????????? ? ?010? ? ?011?0?1010? ????????????????????????????????????????????????????????1??0 Coelurus??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????11100?10111[0 1]1??0?1???10100[1 2]?0[0 1]0?1????????0???000?01?????????????????0???? [0 1]00???????0????1????????[0 1]??????????????????????? ?????????0? ?????20121?011??2[0 1][1 2]111000?00???????0001??????000000??????????????????????????????????????1110???1????? 1?0??1??0 Compsognathus 00[1 2]00?11?2??????1?1????011001??????1?????0--??0?1??0000????1???0????0??2??0?????????????[0 1]??????1???0??01????????????????????0000???1?0??0????1??0?11100?0?1???10??00??0[0 1]0?????010??????????0?0??000?01?10?01?00--?011??0?00???0??00?00???11?10?0?????1?000 0[0 1]?10????01????1?2???????????11?00??10000???????????????????2?????0???????????001??0???0?0??2???0??????00??00000? ?00?????????0-0?001??01??1??1???00?000?1??0 18

19 Condorraptor??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????11100? ???1110?11???????[2 3]01??00?0?0?00?201????????????????????????????????????????????????????0???????????000 0???????0000????0??0?01???????[ ]???01?01002?????????????????????0????????101??0???????0????????????????????????????????????????????????????????????? Confuciusornis ?? ? ?????---00??0--?01?1??0110??? ??01??00?0?0000[0 1]0??-?????1?????????????????????2?????? ??1?0?00?1??????????00?0??1?0?0??01?0 1[1 2][0 1]?1?-?100?11?30??10?1?1010?0??????11? ? ?1100?? ? ?--?0?1201?0-0? ?412?10???????????? ?1? ???1?????0??0??????00??0?00?? ???????????????????????????????????????1??2 Cryolophosaurus 10[1 2]????????????????????????????????0?010?111?20?1? ?????000?0???00?????????????? ?????11100[0 1]0?0??0??0?00?00[0 1]0???1010??010???1?00????0?0?00000???????????????????00??0?00??????????????????????? 0????0??01????0?1??0?0000??????0????0? ????10[1 2]10??? ???????????????????000?0000????000? ?????0???????????????1?000???????0??100? Deinonychus 0? ???00????1100??1? ?0100[0 1]01???? ??100112???????010000??? ????0?0?1????????0?1????????1[0 1]11311??? ?00?0-?1??1?? ?20??01?01211?? ?????1???1? ???????10?1? ?110? ? ???0??0?111011?21?????312110??101????1? ? ?0000????1000?0101??????0101?00??110010????????11000?1100 Deltadromeus????????????????????????????????????????????????????????????????????????????????????????????????????????????1???????????????????1???0?0?1????????????????????????????????????????????????????????????????1???????????????0??1?????11????1?111???????0???????0??0??????????????????????????????????????????????????????????01?????110? Dilong ??????021? ??00? ?21? ?0?[1 2] ?[0 1]? ?1210-?1?[0 1]01?0?0?000?00021?1???0?????????? ?110?1??11??????11100?0?010010??01??0[1 2]0?????0[0 1]??????????????10???????0??????0??? ?0?0???????? ?0?00??001110???1100??????1000??[1 2]0??11000??100[0 1][0 1]?11??20??????101??????0??????????????00????????????2??????????00?? ?0???0??0???0??0?????????????????????????0 Dilophosaurus_sinensis 1?2120[0 1][0 1]0[1 2]????1??[0 1]? ??1??0??11?1111?20????10?000001? ? ?0???00???1????????????????????????????0??????????????????????????????????????????????????????????????????????????????????????????????????????????????? Dilophosaurus_wetherilli 101?11111[1 2] ?010100? ?111?20?10??0?0?0?0101??000? ?0?01?00? ? ?100000??0?????0?001001?? ? ? ?1 19

20 000? ? ?000????????000? ??? ? ? ? ? ? ??1?0??0?10000?0100???000???00?00?0?01????00??? ?1000 Dracovenator????1101?2? ???[1 2]1??1???????0??????????????????????????????????????????????????????????????????????????????????????????????????0??1111???????????????????????????????????????????????????????????????????????????????????????????????? Dubreuillosaurus 1? [1 2]0?0???001100? ?100000????????210????000001?11100? ? ??[1 2]01000?0? ?1?000?0????02????? ???????????????111???0???????????1??1?10???1????00[2 3]0?0000?0?0?0??01?0?0??????????1100?0[0 1]????????0???????????????????0?00????????????????????????????????????????0?0012????[0 1]0??????????01???????????????????????????20?????????00??00???? ?0????0???00?0?00??1?????????????????????? Ekrixinatosaurus???????????????????????0???0??????0?????????????????????????????1???1??????111?????????????????????????????????????????????????????????????????????????????1?1? 01???????1????????????[1 2]???0??????????1???????????????????????????????????????????????????????1??1?????1???1????????????0??????????????????????????1??1???????????0?1???1?????????????0????????????1??1??1???00??1??????1???????????10??001??????0??????11?11?? Elaphrosaurus??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????10[0 1]00[1 2] ?00???021011? ?-110?0?000?010?????????????0?? ???0????????????0????????011? ?0???0? ??1???100?1100?? ?0??????????0?????????????????????????????????????? ? 01??111010?10?? Eustreptospondylus ?1020?0???00110?? ?????????????10000?01?1100?????001100????001???0?0?201????0???00001?110000?????????0??01?011???????????? ? ???1001?1?10??000?0????0?000???000??????????????1?0???? ?????????????????????????0????01?0100?0100?11??0?10??100?0???00??011? ?0110? ??2????0?100???1??0??0????0????????????????????????????????????????????????????????????? Giganotosaurus 102????1????????00??00?110000?11? ?0--?2???? ??11?10?? ???????0?0?011? ?0???? ????[1 2]??????2000????1???? ?0[0 1]?101200?00???21???1010??1??20?? ?000100??????????? ????????????????????????????????0100?01?01??10100?10?? ??0??1010? ?? ??0110???1??????????????????????????????0????????????????????????????????????????????????????????????? Ilokelesia??????????????????????????????????????????????????????1?????????????1?0?01??????????0?0????????????????1??????????????????????????????????????????101?0?0[0 1] ?0211?[0 1]1???1?1???111????????0?1??0?200?00?????????????????????????????????????????????????????1?1????????1??????????101??????????????????????1010?????011??????????? Irritator 20

21 1?20????12???????????? ??2??1??011100?20?0? ??000000??000010?? ?? ?10?1001?0???????????0????1??110?????????????????????????????????????????????????????????????????????????????????????????????????????????????????0????????????????????????????????????????????????????????????????????????????? Liliensternus?????????[1 2]?????????????01??1??0????00?????????0?1??????????????????????000?0????1???0?0?100??? 0??????????????????????1?10???1001???0?????????????? ?100011?? ?0???0??0000??000??0??????????? ?00???0???1????0????0?00000??0?? ?00000? ? ?0?? ?1??0??0000?00??????????????????????????????????????11?0???????????01????? Limusaurus ?4-2[0 1]? ?210?01100??---000[0 2]0--?0??1? ??-0??? ?????????????????????????????????????????????0? ??00?000??1?0110?10100?1?0?0000?000?00?2?????100??????????0?0? ?1100?--1 0? [0 1] ?110-? ?100?1?2?????000? ?10000??2???0?0????????????100??1?1?????001110??00???12? ?-001? ?00?????????1?? ?1??? ?101??1 Majungasaurus ? ? ?0?020100?1?000000?10?101?10?110? ? ?10?? ?1?100?11131??110???0???12?0??0?????????011??1??11?101??????????????????????????01000??0?1100?121?20011??????????????????0???2?1??????1?11?2???11?11?1?111? 1??0??0?01????1??1?1?????0? ??111??1 Mapusaurus 1???????????????????00? ??10--?21?1011? ????????0?01?????????????100???????????????????????????????????200?111?10010?1????? ??? 21??01?1000??0???????? ???0?????????1?00????1??0?00???0???????0?0???????0? ????100101?01??000????????0?00? ? ? ?0?111???0?1 0? ??0???????0????????????????????????????????????????????????????????????? Masiakasaurus?0????????????????1????110010?01112?0?????????????????0?0???????0???0??0 00???????????????????????0?????1???????????????? ?00?????????11?0? ???000? ??[2 3]0??11??0?0?00010?????????????0????1??11010???????????????????????0?000????????????0?2??2?? ??????1?? ?210? ?0??10 0??0??1??1?10????0?01?1?1?? ?????1?101??? ?111101??1??1?1121? Megaraptor??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????10111?01? ???????????????????????1?0?????0??00???????????0?000100???????00? ? ?????????????0?0??????00[1 2]0011?????????????????????????????????????????????????0????????101??????1111?0???????????????????????????????????????????????????????????? Monolophosaurus 1? [1 2]??0011?0? ?1000??11?1101?21? ? ? ?10??00??0??????? ?10????0??1?1110??0?01?020?000?0001?0?1?100??0020????0?0?0???0???????????????????????????????????????????????????????010? ??[0 1] ?0000???00? ???0????????????????????????????????????????????????????????0?10? ? ????1????00?00?0?00?????00?0??????????0 21

22 Neovenator?0?? ??0?100? ?00000?1010--????????????????????????????????????????????????????????????????????????????????0?00??????????????????1??????????????0????021?0?1?100010???????0?0?0?010??10?0??????????1??????????????????????????????????????010??????1??1?1?0??00?0?[1 2]00?100??0?10? ?010120?2??01100???????????0??00?00?101120??0????0?0???00??????????????????????????????????????????????????1??0 NMV_P186076??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????00?0?????????????????????????????111??0???????????????????????????????????????????????????????????? Noasaurus?????????????????????0?110010? ???????????????????????????????????????????????0???2?????????????????????????????????????????????????????????1[0 1]10?[1 2]0?? ??0????????????????????????????????????????????????????????????????????????0??1???????1????????????0??1?1????????????????????????????11??0?0?????010??????????1 Ornitholestes 0? ???00?121100? ??00??0010--????10100?010?012??000? ? ? ?0????????1?????????????[2 3]?10?00?00011?1000[0 1]0?11??????11100?01?110100?01???101??2?? ??0?0?0?000?0?01?1?????????0???????? ?00??? ??0010?00111?0??? ?1000??200????-?00100[0 1]0??1????111?0??????????01?00??????????00?? ?1??????000?0000??000??1001? ???????????00?0???01?????0?????1000?1??0 Piatnitzkysaurus?????????[1 2]????????????? ????????????????0???????1000?0??????????????????????0100 0??? ?0????????????00?0?????????????011101[0 1] ???1110? ?1100??0????????????????????? ?????????????????????0?0??010?1?? ? ??0?????1??????0?? ??????000?00???????????????????????????????????????????????????????????? Rugops??????????????????1????0???0?????00?1??12????2????????1?1???????0?????????101???????????? ???111????????????????01??????????0????????????? Segisaurus????????????????????????????????????????????????????????????????????????????????0?????????????0??????000???00?000?????????? ??000?0????????????????????0?00 0????????????????02?????010?000????00?0?0?????????10?0??1?????1110?????????????1?00???0???010??00????0?????????????????????????????????????????00???????01?0?????0 Shenzhousaurus????0004-1???0???-??00? ???1-1? ??1-??000??????1-??0000??0????00?0100??-0?-??-?---?????????--????????1??--?? ????1??-?1?????-??-?????--????????-??-[0 1]0???-?10--?-?20??0??-0?00-0??0?01?---??--?-??----?-????-??--??---1??????1???0?? ? [0 1]001[0 1]?00? ? ??????????????????????????????????????-?????????????00?????00??0?0000????????????????????????????0???????00?1?00 Sinornithomimus 00?? ?000??-?1?010??0??0?10?-?? ?0??1?000??10011?? ? ?

23 0001?0010??????????????????0?????????010?01-?1???01?111??0?0?0111?00?01?11?100002?0 1100?0??10?010?30????0???0??001??011???????? ?00??? ???1?0111?1?2?001?200?1000[0 1] ? ?001?00212? ?00?000?0?1[1 2]0?0?000?00???????????????????????????????????????????????????????????0 Sinosauropteryx [1 2]01??????1?1????0??0?1?????01???010--????1??00??????11???????????0?????0?02????10?????????????????????????????????????00???????????????????11?00???1???10??01?002??????010????2?????? ? ? ??00?00?011111[0 1]10111?01001?011100???0100??1?2????0??????10?01??10?000????2[0 1]??0?0?????????????0??12??1????001?00???0????[1 2]0??0?????????????????????????????????????????????????????????????????0 Sinraptor ? ?1110? ?? ?00???10?????1?001100??????????????????????01 0??010??0? ???00? ? ??0?1?0101?000?1000??100???????? Spinostropheus???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????2???0?0?0??0?????0??????????113???1??????????????????????????????????0???1?????????????????????????????????????????????????????0?????????????????????????????1?????????1???????????????????????????????????????????????????????????????????????11011?11?000??????????? Streptospondylus?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????0????????????00???1?01???????????????????????????????????????????????????????????????????????????????????????????????????????????1100????????????????????10?????021????? ????????????????????????????????????????????????????????????????????????????????????? Suchomimus? [1 2]0?01?0010?101200?00-1?2111??0?????????????000?????0???00????0???00???????0????0??????????????????????????????? ???1????????? ??????????2????0??0[0 1]01? ??????????????????0??????????00??? ????????????010?? ?00100[0 1]????1??00?0[1 2]00?00?00?0? ?1?12??2??0110??010?1???????????0???????????110?11???????????????????????????????????????????????????????????? Syntarsus_kayentakae ?010? ?010010? ?10? ??00?1? ? ?0? ?001200? ?? ???????? ? ??0???0??1??????????0???0000?0?00111? ?? ?0? ? ?011?0??020?00????0????????????????????????????????????????????????????????????0 Torvosaurus 1???01000[1 2]0100? ?21?000? ????????2001?100??00101????????001100??????????0?0?2???????????????????????????????????0??0?????????????100?? ? ???211001?1 0001?020????0?0000?000?0?????????????1?????? ??? ??000?? ?00? ? ??10???1???? ?0?? ???????010?00???????????????????????????????????????????????????0?000???0 Tugulusaurus??????????????????????????????????????????????????????????????????????????? 23

24 ???????????????????????????????????????????????????????????????????????11??????1????0?0 0??????????????????????????????0?????????001012??101?? ?????20[0 1] ???????????????0??????0??????????????????????????????????????????????????????????1000 Tyrannosaurus ?000? ? ? ? ? ??1????? ?? ??1?1?? ? ?? ? ??0? ?1??10?1? Tyrannotitan?0?????????????????????????????????0?????????21[0 1]1?????????????????????????????????1?????????????????????????????????????????2000??????????????????10111? ???21?0?1?100010?[2 3]?????0?0????00??1??????????????000100???????0[0 1]???????????????????????0??000?????????????????0?0011??00[0 1][0 1]1010?012? ????????????00???????????????0?????????0?[0 1]0????0??0??????????????????????????????00?????0??????????0?1??01??? Velociraptor [0 1]010?000?? ? [0 1] ? ?11311? ?1?00000?1?01??1?11100??101?????0?1??111? ?1? ?? ?? ? ? ?

25 ? ?010000??00??0000?? ???????????????????????????????01?????1000 Zupaysaurus 0?10?????[1 2]?????1?????? ??1?010?000?110?20?101? ? ?????0??????????????????????? ???010?10?11????0?????????????????0??????????????????????????????????????????????????????????????????????????????????????????????1????????????????????????????????????????????00????10111???? ????????????????????????????????????????????????????????????????????????????????????? 25

26 Analysis and results The data matrix (65 taxa, 413 morphological characters) was assembled using Mesquite v , using character statements from the datasets of Smith et al. 20 and Carrano and Sampson 21. These datasets were selected because of their dense sampling of the Ceratosauria and because they also included theropod taxa that bracket the Ceratosauria. Some characters in these two datasets contained either nested character state sets or three or more states where one state was absent. These characters were considered ordered in our analysis, and are marked as such in the character list. Manual digital characters were scored as I-III for all tetanurans including birds. Phylogenetic analysis of the three data matrices was conducted in TNT 22. Trees were rooted on Marasuchus. The following heuristic search settings were used to generate most-parsimonious trees (MPTs): hold 10,000 trees, 5000 Wagner builds, retain 3 trees per replication, with tree bisection and reconnection (TBR) as the search strategy. Heuristic searches recovered 1882 MPTs of length The strict consensus tree is shown in Figure S4. The taxa (Limusaurus + Elaphrosaurus), Deltadromeus and Spinostropheus are unresolved at the base of Ceratosauria. It is likely that Spinostropheus is closely related to Elaphrosaurus, based on the presence of a dorsal diapophyseal fossa on each cervical bertebra 21. More skeletal remains of Spinostropheus would likely help resolve its position. Deltadromeus was initially described as a coelurosaur, but was assigned to the Ceratosauria by Carrano and Sampson 21. Its basal position in our phylogeny is in accord with their results. The basal position of Deltadromeus may, however, reflect a lack of character data. Personal inspection of Deltadromeus was outside the scope of this research and we were thus unable to score many of the characters derived from the Smith et al. matrix. Elaphrosaurus and Limusaurus are recovered in all MPTs as sister taxa, although they share only one synapomorphy in this data matrix: cervical ribs fused to their corresponding vertebrae. This character is also present in more derived ceratosaurs (including Ceratosaurus), and this sister-taxon relationship is likely to be labile given more character data for Elaphrosaurus. Further osteological comparisons between Elaphrosaurus, Deltadromeus, Spinostropheus and Limusaurus are needed to resolve phylogenetic relationships at the base of the Ceratosauria. The following synapomorphies support the monophyly of the Ceratosauria in some or all of the fundamental cladograms: Synapomorphies for the Ceratosauria: 41.2, 56.1, 75.2, 152.2, 182.3, 186.1, 187.1, 220.1, 225.1, 273.1, 282.1, 290.1, 336.1, 398.1, 404.1, 407.1,

27 Figure S4. Strict consensus of 1882 most parsimonious trees (tree length = 1093, CI=0.44, RI=0.74) 27

28 7. Quantitative analysis of digital homologies The problem of digital homologies is an example of the larger problem of homologizing serially repetitive structures, such as vertebrae. Multiple hypotheses of primary homology 23 specifying the structures considered to be homologous may be possible, and a choice is typically made prior to a phylogenetic analysis on the basis of the similarity of the structures in position, composition, and connectivity 24. A quantitative method of evaluating correspondences of repeated morphological structures between taxa is suggested by comparison with sequence alignment of molecular sequences when sequence length varies 25, 26. When different alignments of nucleotide or amino acid positions have different phylogenetic implications the alignments may be tested by congruence with other characters on a phylogeny 27. The problem of alternative primary homology statements with the same phylogenetic implications has been little discussed, but can be addressed in the same framework. The problem of digital homologies in theropods is complex because the developmental and contextual information for one taxon extant birds is much more detailed than for extinct taxa. This information strongly implies that living bird digits are II-III-IV 28, whereas the digits of non-avian theropods are interpreted as I-II-III(-IV-V) based exclusively on the morphology of adult skeletons. The digital homologies of basal theropods are unproblematic because Herrerasaurus, Eoraptor, Coelophysis bauri 16 and Dilophosaurus (see above) have five digits (although V comprises only a small metacarpal). In Ceratosauria, however, a manual digit is completely lost, and thus the four remaining digits could correspond to positions I-II-III-IV or II-III-IV-V of the primitive theropod manus, if digit loss is restricted to the anterior and posterior margins of the hand. In tetanurans, if digit loss is constrained to the anterior and posterior margins of the manus, the three digits of these taxa could correspond to positions I-II-III, II-III-IV, or III-IV-V, but the presence of a fourth digital laterally in some taxa (e.g., Guanlong, Sinraptor) contradicts the latter hypothesis. Assuming birds are 2-3-4, it is possible to compare alternative "alignments" of digits in other theropods to evaluate the set of primary homologies that maximizes hypotheses of homology and minimizes homoplasy. To address this question, we constructed several data matrices with alternative codings for the digital homologies in theropods. We identified a set of 24 morphological characters and scored these characters for each digit present in the 121 taxa in our analysis (see below). Taxa with five digits therefore were scored for 120 characters. Taxa with fewer than five digits could only be scored for a reduced number of characters, the others were scored as absent or inapplicable. We added these characters (hereafter dynamic characters ) to 397 non-digital characters that did not change their correspondences across datasets (hereafter static characters ) to create separate matrices of equal numbers of characters and taxa that implied differing correspondences between the digits of theropods. Consideration of all possible primary homology statements for theropod digits is numerically unfeasible given the current lack of appropriate software, a problem also encountered by Ramirez (2007). Thus, for practical reasons we only considered the following subset of the possible alignments in this analysis: those implied by shifting topological identity from I-II-III to II-III-IV at various nodes on the theropod tree (schemes 1-11; shown by hollow boxes number 1-11 in Figure S5); a set of correspondences (scheme 12) that aligned the three digits of birds with I-II-III of the tetanuran manus (although this situation is unlikely given the wealth of developmental studies supporting extant birds as II-III-IV 28 ); a scenario where the digits of ceratosaurs and non-paravian tetanurans are I-II-III-(IV) and those of paravians are III-IV-V (scheme 13); and a scheme where the digits of ceratosaurs are I-II-III-IV, those of tetanurans are 28

29 II-III-IV-(V), and those of paravians are III-IV-V (scheme 14). We did not test alignments that involved loss of the middle digit (e.g. Tetanurans are I-III-IV-(V)). Figure S5. Simplified phylogeny of the Theropoda derived from the analysis in this paper. Hollow squares represent locations of possible shifts in digital correspondence, numbers adjacent to squares are cited in the Figure S6 and in the text. Figure S6. Graph of lengths of most parsimonious trees by correspondence scheme. Correspondence scheme numbers 1-11 (x-axis) are equivalent to node positions on generalized theropod tree shown in Figure S5 and all correspondence schemes are detailed in Table S

30 Shortest tree length (2351) marked by green diamond. Shortest tree length (2357) when Aves are considered II-III-IV marked by a red diamond. Two basic matrices are supplied in the supplementary information for this study: the I-II-III matrix codes the fingers of all theropods with fewer than five digits as corresponding to positions I-II-III(-IV) and the Tetanura II-III-IV matrix codes the fingers of all Tetanurae as corresponding to positions II-III-IV(-V). All other matrices analyzed in this study were created using the I-II-III matrix by selecting the descendants of a given node on Figure S5 (constituent species of taxon groups used in this study are indicated in bold in the supplemental matrices), and moving the character scorings laterally by one digit. For example, invoking a correspondence shift at the base of Paraves (node 10, Fig. S5) would involve selecting the characters scored for digits I-III of Dromaeosauridae, Troodontidae and Avialae (characters numbered ; for character number/digit identity see supplementary table 1) and moving them laterally to the character positions for digits II-IV (characters numbered ) in all subtended taxa. This shift implies that digits I and V are absent, therefore characters 398 and 494 (Digit X: absent (0); present (1)) should then be scored as absent and characters and scored as inapplicable (-). Digital position Characters Digit I Digit II Digit III Digit IV Digit V Table S1. Digital position and related character numbers in this study. Digit number is with reference to the primitive theropod manus, thus Digit I corresponds to the thumb (medial digit) of Herrerasaurus. Characters numbered as if character set starts at 1, the default setting in Mesquite 19. Analysis protocol and results Phylogenetic analysis of the matrices was conducted in TNT 22, using heuristic algorithms designed for large datasets 29. We used a driven search strategy, stabilizing the consensus twice with a factor of 75, and employing the following heuristic search techniques with default settings: sectorial search, ratchet, tree drift, tree fuse. The most parsimonious tree lengths and number of trees for each alignment are shown in Tables S2 and S3 using ordered characters and unordered characters, respectively. Following Makovicky et al. 30, we considered Neuquenraptor argentinus a junior synonym of Unenlagia comahuensis. The results of our ordered phylogenetic analyses (Table S2) show the shortest length trees are produced using the correspondence scheme where the digits of all theropods are I-II-III. However, as discussed in the text this correspondence scheme is not preferred because it does not explain the available ontogenetic information for the homology of the avian digits. When birds are scored as II-III-IV, the optimal correspondence scheme is produced when the digits of all Tetanurae are identified as II-III-IV(-V) (node 2 in Fig. S5; results summarized in supplemental table S2). This scheme produced 114 most-parsimonious trees (MPTs) of length 2357, CI= 0.25, RI= Using this correspondence scheme, 62.5% of the manual digital characters are 30

31 informative. A correspondence shift from a I-II-III to a II-III-IV identity at the base of Tetanura (node 2 on Fig. S5) is 10 steps shorter than the shortest alignment in which the shift occurs within Tetanura, and four steps shorter than invoking a similar shift at the base of Ceratosauria. This correspondence scheme is six steps longer than when birds and other tetanurans are I-II-III. Correspondence schema where paravians were considered III-IV-V and non-paravian tetanura either as I-II-III and II-III-IV were 14 steps longer than the preferred alignment scheme. To test whether our character ordering was influencing our phylogenetic results, we reanalyzed each alignment scheme with the characters unordered (results in Table S3). Although the length of the most-parsimonious trees produced without character ordering differed from the ordered analysis, the general pattern of tree length under different alignment schema did not. One notable observation is that without character ordering, the lengths of the MPTs under a Tetanura II-III-IV (node 2) alignment scheme (2286 steps) were the same as the lengths of the MPTs under an alignment scheme where all theropods were I-II-III-(IV)-(V). The phylogenetic relationships recovered using the unordered analysis (not shown) were fully compatible with those produced using ordered characters, although several groups differed in degree of resolution between the two datasets. Correspondence scheme Length of Most Parsimonious Trees * All theropods I-II-III (scheme 12) Paraves III-IV-V (scheme 13) Paraves III-IV-V, Tetanura II-III-IV-(V) (scheme 14) Number of Most Parsimonious Trees Table S2. Results of phylogenetic analyses using ordered characters under different alignment schema. Data also depicted in Figure S6. Correspondence schemes refer to node numbers of Figure S5 (see supplemental text for explanation). Scheme with shortest MPTs shown in bold. Correspondence scheme entitled all theropods I-II-III refers to a set of correspondences where the digits of Avialae are considered positionally homologous to digits I-II-III of the primitive theropod manus. *Alignment where Ceratosaurs are I-II-III-IV and Tetanurans are II-III-IV-(V). 31

32 Length of Most Number of Most Correspondence scheme Parsimonious Trees Parsimonious Trees * All theropods I-II-III (scheme 12) Paraves III-IV-V (scheme 13) Paraves III-IV-V, Tetanura II-III-IV-(V) (scheme 14) Table S3. Results of phylogenetic analyses using unordered characters under different alignment schema. Correspondence schemes refer to node numbers of Figure S5 (see supplemental text for explanation). Schema with shortest MPTs shown in bold. Correspondence scheme entitled all theropods I-II-III refers to a set of correspondences where the digits of Avialae are considered positionally homologous to digits I-II-III of the primitive theropod manus. *Alignment where Ceratosaurs are I-II-III-IV and Tetanurans are II-III-IV-(V). The strict consensus of the trees when tetanurans are II-III-IV (scheme 2; Fig. S7) shows poor resolution for the Ceratosauria. Evaluation of the fundamental cladograms, however, reveals that Elaphrosaurus is an unstable taxon, grouping variously with all ceratosaurian taxa. This instability is likely due to the lack of complete skeletal material for Elaphrosaurus and the variability of axial characters within the Ceratosauria. A reduced consensus 31 with Elaphrosaurus removed (Fig. S8) groups Limusaurus sister to Masiakasaurus at the base of the Ceratosauria. This is a novel phylogenetic position for Masiakasaurus, which was previously recovered as a noasaurid 21, 32, 33. New information on the Masiakasaurus skeleton (Carrano, personal communication) will hopefully clarify this uncertainty. The oviraptorosaurian taxon Hagryphus was also removed from the reduced consensus, as its phylogenetic position was highly variable within Oviraptorosauria, Dromaeosauridae and Troodontidae in the fundamental cladograms. Synapomorphies for key groups of interest are shown below (the following unambiguous synapomorphies diagnose their respective clades in all fundamental cladograms): Ceratosauria : Char. 3: 0 --> 1 Char. 10: 0 --> 1 Char. 72: 0 --> 1 Char. 257: 0 --> 1 Char. 268: 0 --> 1 Char. 329: 0 --> 1 Char. 373: 0 --> 1 Char. 394: 0 --> 2 Tetanurae: Char. 36: 0 -->

33 Char. 50: 0 --> 1 Char. 141: 0 --> 1 Char. 190: 0 --> 1 Char. 210: 0 --> 1 Char. 289: 1 --> 0 Char. 358: 1 --> 2 Char. 367: 1 --> 0 Node 4 (Ceratosauria + Tetanura) (see figs. S7 and S8) Char. 22: 0 1 Char. 114: 0 1 The following unambiguous characters support a sister-group relationship between Masiakasaurus and Limusaurus (node 3, Fig. S8), but in some fundamental cladograms also support the inclusion of Elaphrosaurus as sister to either taxon: Char. 131: 0 1 Char. 133:0 1 Char. 252:0 1 Implications for digital homology Based on this study, the most parsimonious alignment is for the four digits of ceratosaurs to be I-II-III-IV and the three (and sometimes four) digits of all Tetanurae to be II-III-IV(V). Accepting such a topological shift at the base of Tetanura requires that the positional homology of the three digits of tetanurans is II-III-IV(-V), as suggested by Wagner and Gauthier 34. Because the four digits of ceratosaurs are therefore most parsimoniously interpreted as I-II-III-IV, the small lateral metacarpal ossification of Guanlong 35, Sinraptor 36, and Coelurus represents the re-ossification of metacarpal V after it is lost at the base of Ceratosauria. The poor phylogenetic resolution for basal tetanurans in our study precludes us from hypothesizing whether this re-ossification event occurred once or more than once in the evolution of Theropoda. Likewise, the fourth metacarpal, which is reduced in primitive theropods and bears an unknown number of phalanges in Ceratosauria, re-acquires at least three phalanges in Tetanurans. 33

34 Figure S7. Strict consensus of 114 most-parsimonious trees depicting phylogenetic relationships within Theropoda, when the tetanuran manus is scored as II-III-IV. All fundamental cladograms are length 2340, CI=.25, RI=.64. Labeled ovals refer to nodes of interest (see text). Labeled ovals refer to nodes of interest (see text). 34

35 Figure S8. Reduced cladistic consensus cladogram 11 of 114 fundamental cladograms depicting phylogenetic relationships within Theropoda. Taxa removed from cladogram are Elaphrosaurus and Hagryphus. 35